1. Process to find variable

Hi,

Based on the info in the attached image, how would i be best going about finding the value for kappa?

The value for kappa is given as 2d^2k, but I'm unsure how it comes to that.

Thanks,

Ling-pau

2. Re: Process to find variable

As the front end of the car dips down a small angle $\theta$, the linear displacement, $\Delta s$, of spring #1 (a stretch) is approx $d \cdot \theta \implies F_{s_1} = -k \Delta s = -k d \theta$.

The same happens at spring #2 (a compression), so $F_{s_2} = -k d \theta$.

Overall torque on the platform is $\tau = d \times 2F = d \cdot (-2k d\theta) = \color{red}{-2kd^2} \theta = \color{red}{-\kappa} \theta$

3. Re: Process to find variable

Nice one, thank you. Makes much more sense now!